More single U.S. women over the age of 35 are having children, even as the overall birth rates for unmarried women in the United States have dropped, the Centers for Disease Control and Prevention said on Wednesday.

Running counter to the trend were middle-aged and older women having children outside of marriage. The birth rate for unmarried women between the ages of 40 to 44 increased 29 percent from 2007 to 2012 and 7 percent during that time for those aged 35 to 39, the CDC said.

"Many women are postponing births until their 30s, and the stigma of having a child outside of marriage has faded," said Andrew Cherlin, a sociology professor at Johns Hopkins University who has studied the issue but was not involved with the CDC report.

Women who choose to give birth at an older age now have greater medical options for increasing fertility, said Sally Curtin, a CDC statistician and an author of the study.

"There's more out there for women to meet their fertility goals," she said.

About 40 percent of children in the United States are born to unwed mothers of all ages, the CDC said.

Still, the birth rate among all unmarried women has dropped from a peak in 2008 of 51.8 babies per 1,000 women to 44.8 babies per 1,000 women in 2013, a 14 percent decline.

The largest decreases were among teenagers and black and Hispanic women, data showed.

Birth rates for married women also have dropped, but not as rapidly, the federal health agency said. The study analyzed statistics but not the causes of changes in births rates.

The percentage of unmarried women who give birth while living with a partner increased to almost 60 percent in 2010 from 41 percent in 2002, a shift that could indicate increasing financial and social support from fathers for mothers and children even without marriage, the study said.

There is debate, however, over the benefits of co-habitation.

"More research needs to be done about the implications for the child and the family," Curtin said. "Studies have shown that cohabiting relationships do not last as long as marriage."

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